Problem 99 - Introductory Algebra for College Students

Question

How do you determine whether an ordered pair is a solution of an equation in two variables, \(x\) and \(y ?\)

Step-by-Step Solution

Answer

To determine if an ordered pair is a solution to an equation, substitute the x and y values from the ordered pair into the equation. If the resulting simplified equation holds true (the left-hand side equals the right-hand side), then the ordered pair is a solution of the equation.

Step 1: Understand the question

The question is asking if a specific ordered pair (x, y) is a solution to an equation. A solution to an equation is a set of values for the variables in that equation that make the equation true. If an ordered pair is a solution, substituting the x and y values from the pair into the equation should result in a true statement.

Step 2: Substitute the ordered pair into the equation

Take the given ordered pair, which will be in the form (x, y) where x is the first value and y is the second value. Substitute these values into the given equation in place of x and y.

Step 3: Simplify the equation

After substituting x and y values into the equation, simplify it. This may involve multiplication, addition, subtraction, or division, depending on the specifics of the equation.

Step 4: Check if the equation holds true

After simplifying the equation, observe if the equation holds true. That is, verify if both sides of the equation are equal. If they are, the ordered pair is a solution of the equation. If they aren't, the ordered pair isn't a solution.